Question

Diagonals AC and BD of trapeziem ABCD with AB/DC intersect each each at O.
prove that area (ADD) = area (BOC)
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Answer 1

Step-by-step explanation:

Given: Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. 

 

To Prove:

ar (AOD) = ar (BOC).

Proof:

Here,△DAC and △DBC lie on the same base DC and between the same parallels AB and CD.

∴ ar(△DAC) = ar(△DBC)

 ar(△DAC) − ar(△DOC) =ar(△DBC) − ar(△DOC)

 

[On subtracting ar(△DOC) from both sides]

ar(△AOD) = ar(△BOC)

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